C₄⁴⋊C₅ #13046041

order	1280
isoclinism	isoclinic class of C₄⁴⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₅ · Schur multiplier (H₂) = C₄²

Aliases

C₄⁴⋊C₅

C₄⁴ ⋊ C₅

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₄⁴	C₅
Frattini, socle	C₂⁴	C₂⁴⋊C₅
LCS	G ▷ C₄⁴
UCS	C₁

402 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 20

Polycyclic presentation:

5,2^8|b^2=f,c^2=g,d^2=h,e^2=i,b^a=beh,c^a=cdf,d^a=bdgh,e^a=cgi,f^a=fi,g^a=gh,h^a=fh,i^a=g

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1116309);